We show that in any bipartite tournament with no transmitters and no 3-kings, the number of 4-kings is at least eight. All such bipartite tournaments having exactly eight 4-kings are completely characterized.
Kings in bipartite tournaments
โ Scribed by Vojislav Petrovic
- Publisher
- Elsevier Science
- Year
- 1997
- Tongue
- English
- Weight
- 499 KB
- Volume
- 173
- Category
- Article
- ISSN
- 0012-365X
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โฆ Synopsis
We present a variety of results concerning characterization, number, distribution and some aspects of stability of r-kings (r = 2 4) of bipartite tournaments.
๐ SIMILAR VOLUMES
Let T be an n-partite tournament and let k,(T) denote the number of r-kings of T. Gutin (1986) and Petrovic and Thomassen (1991) proved independently that if T contains at most one transmitter, then k4(T) >i 1, and found infinitely many bipartite tournaments T with at most one transmitter such that
A digraph D is said to satisfy the condition O(n) ifd~-(u) + d r (v) >t n whenever uv is not an arc of D. In this paper we prove the following results: If a p x q bipartite tournament T is strong and satisfies O(n), then T contains a cycle of length at least min(2n + 2, 2p, 2q}, unless T is isomorph
Petrovic, V. and C. Thomassen, Kings in k-partite tournaments, Discrete Mathematics 98 (1991) 237-238. We prove that every k-partite tournament with at most one vertex of in-degree zero contains a vertex from which each other vertex can be reached in at most four steps.